Confusion about relativity of simultaneity I am an engineer currently doing some self-study of physics in my spare time.
While learning about the relativity of simultaneity I have come across 2 different example problems that seem to give contradictory results. Both examples deal with an observer on a moving train and a second observer stationary on the platform.
Example 1 has a light source at the center of the train
Example 2 essentially has 2 light sources, as both ends of the train are struck with lightning bolts at t=0
The solutions given for these problems, in the reference frame of the observer on the train, seem to be contradictory. In example 1, the light reaches both ends of the train at the same time, where as in example 2, the 2 lightning flashes do not reach the center of the train at the same time.
How is this not contradictory? In both examples, light in the reference frame of the observer on the train has to move L/2 and has speed c. What am I missing here?
In my mind, if you place mirrors on the ends of the train car and you run the scenario for twice as long, then example 1 becomes example 2, with the light pulses being reflected back to the middle of the train.
Any help understanding this would be much appreciated.
 A: Marco already answered, but let me rephrase it in light of the examples.
In example 1 the simultaneity of light reaching both ends of the train is with respect to observer at rest with the train (called Marvis in example 2). In particular, they are not simultaneous with respect to observer at the ground (called Stanley in example 2)
In example 2, the lightening bolts strike ends of the train simultaneously with respect to Stanley and thus they will not be simultaneous with respect to Marvis. In example 1 this was the other way around, so the two examples are different. And since the two lighting bolts did not strike the ends of the train with respect to Marvis at the same time, they will also not arrive to the center at the same time, even thought this statement of yours

In both examples, light in the reference frame of the observer on the train has to move L/2 and has speed c

is correct.
A: When you say that in example 2 both ends of the train are struck at t=0, if t is the time on the train then the flashes will reach the centre of the train at the same time- however, if t is the time on the platform, they won't, because the times at either end of the train, in the train's frame of reference, are out of synch with the time of clocks on the platform.
To unpack this a bit more...
If the light from each strike meets at the centre of the train, then from the point of view of the people on the train, the two ends must have been struck at the same time, as both flashes have travelled L/2 in their frame.
However, from the perspective of the people on the platform, the centre of the train is moving forward, so the light from the front strike has travelled less that L/2 to reach the centre, while the light from the rear struck has travelled more than L/2. The only way that can happen is if the rear strike was earlier than the front one.
So, imagine that it is 12 O'clock train time when each end of the train is struck, and that there are clocks all along the platform. An observer at the front of the train, looking out, would see that the clock next to them on the platform was showing just after 12 O'clock, while an observer at the rear of the train would see that the clock next to them on the platform was showing just before 12 O'clock. The observers on the train would conclude that the clocks on the platform  were out of synch. Observers on the platform would believe that their own clocks were in synch, and that the clocks on the train were out.
